mirror of
https://github.com/paboyle/Grid.git
synced 2024-11-14 09:45:36 +00:00
264 lines
8.0 KiB
C++
264 lines
8.0 KiB
C++
/*************************************************************************************
|
||
|
||
Grid physics library, www.github.com/paboyle/Grid
|
||
|
||
Source file: ./lib/algorithms/iterative/FlexibleGeneralisedMinimalResidual.h
|
||
|
||
Copyright (C) 2015
|
||
|
||
Author: Daniel Richtmann <daniel.richtmann@ur.de>
|
||
|
||
This program is free software; you can redistribute it and/or modify
|
||
it under the terms of the GNU General Public License as published by
|
||
the Free Software Foundation; either version 2 of the License, or
|
||
(at your option) any later version.
|
||
|
||
This program is distributed in the hope that it will be useful,
|
||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||
GNU General Public License for more details.
|
||
|
||
You should have received a copy of the GNU General Public License along
|
||
with this program; if not, write to the Free Software Foundation, Inc.,
|
||
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||
|
||
See the full license in the file "LICENSE" in the top level distribution
|
||
directory
|
||
*************************************************************************************/
|
||
/* END LEGAL */
|
||
#ifndef GRID_FLEXIBLE_GENERALISED_MINIMAL_RESIDUAL_H
|
||
#define GRID_FLEXIBLE_GENERALISED_MINIMAL_RESIDUAL_H
|
||
|
||
namespace Grid {
|
||
|
||
template<class Field>
|
||
class FlexibleGeneralisedMinimalResidual : public OperatorFunction<Field> {
|
||
public:
|
||
bool ErrorOnNoConverge; // Throw an assert when FGMRES fails to converge,
|
||
// defaults to true
|
||
|
||
RealD Tolerance;
|
||
|
||
Integer MaxIterations;
|
||
Integer RestartLength;
|
||
Integer IterationCount; // Number of iterations the FGMRES took to finish,
|
||
// filled in upon completion
|
||
|
||
GridStopWatch MatrixTimer;
|
||
GridStopWatch PrecTimer;
|
||
GridStopWatch LinalgTimer;
|
||
GridStopWatch QrTimer;
|
||
GridStopWatch CompSolutionTimer;
|
||
|
||
Eigen::MatrixXcd H;
|
||
|
||
std::vector<std::complex<double>> y;
|
||
std::vector<std::complex<double>> gamma;
|
||
std::vector<std::complex<double>> c;
|
||
std::vector<std::complex<double>> s;
|
||
|
||
LinearFunction<Field> &Preconditioner;
|
||
|
||
FlexibleGeneralisedMinimalResidual(RealD tol,
|
||
Integer maxit,
|
||
LinearFunction<Field> &Prec,
|
||
Integer restart_length,
|
||
bool err_on_no_conv = true)
|
||
: Tolerance(tol)
|
||
, MaxIterations(maxit)
|
||
, RestartLength(restart_length)
|
||
, ErrorOnNoConverge(err_on_no_conv)
|
||
, H(Eigen::MatrixXcd::Zero(RestartLength, RestartLength + 1)) // sizes taken from DD-αAMG code base
|
||
, y(RestartLength + 1, 0.)
|
||
, gamma(RestartLength + 1, 0.)
|
||
, c(RestartLength + 1, 0.)
|
||
, s(RestartLength + 1, 0.)
|
||
, Preconditioner(Prec) {};
|
||
|
||
void operator()(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi) {
|
||
|
||
psi.checkerboard = src.checkerboard;
|
||
conformable(psi, src);
|
||
|
||
RealD guess = norm2(psi);
|
||
assert(std::isnan(guess) == 0);
|
||
|
||
RealD cp;
|
||
RealD ssq = norm2(src);
|
||
RealD rsq = Tolerance * Tolerance * ssq;
|
||
|
||
Field r(src._grid);
|
||
|
||
std::cout << std::setprecision(4) << std::scientific << std::endl;
|
||
std::cout << GridLogIterative << "FlexibleGeneralisedMinimalResidual: guess " << guess << std::endl;
|
||
std::cout << GridLogIterative << "FlexibleGeneralisedMinimalResidual: src " << ssq << std::endl;
|
||
|
||
|
||
PrecTimer.Reset();
|
||
MatrixTimer.Reset();
|
||
LinalgTimer.Reset();
|
||
QrTimer.Reset();
|
||
CompSolutionTimer.Reset();
|
||
|
||
GridStopWatch SolverTimer;
|
||
SolverTimer.Start();
|
||
|
||
IterationCount = 0;
|
||
for (int k=0; k<MaxIterations; k++) {
|
||
|
||
cp = outerLoopBody(LinOp, src, psi, rsq);
|
||
|
||
// Stopping condition
|
||
if (cp <= rsq) {
|
||
|
||
SolverTimer.Stop();
|
||
|
||
LinOp.Op(psi,r);
|
||
axpy(r,-1.0,src,r);
|
||
|
||
RealD srcnorm = sqrt(ssq);
|
||
RealD resnorm = sqrt(norm2(r));
|
||
RealD true_residual = resnorm / srcnorm;
|
||
|
||
std::cout << GridLogMessage << "FlexibleGeneralisedMinimalResidual: Converged on iteration " << IterationCount << std::endl;
|
||
std::cout << GridLogMessage << "\tComputed residual " << sqrt(cp / ssq) << std::endl;
|
||
std::cout << GridLogMessage << "\tTrue residual " << true_residual << std::endl;
|
||
std::cout << GridLogMessage << "\tTarget " << Tolerance << std::endl;
|
||
|
||
std::cout << GridLogMessage << "FlexibleGeneralisedMinimalResidual Time breakdown" << std::endl;
|
||
std::cout << GridLogMessage << "\tElapsed " << SolverTimer.Elapsed() << std::endl;
|
||
std::cout << GridLogMessage << "\tPrecon " << PrecTimer.Elapsed() << std::endl;
|
||
std::cout << GridLogMessage << "\tMatrix " << MatrixTimer.Elapsed() << std::endl;
|
||
std::cout << GridLogMessage << "\tLinalg " << LinalgTimer.Elapsed() << std::endl;
|
||
std::cout << GridLogMessage << "\tQR " << QrTimer.Elapsed() << std::endl;
|
||
std::cout << GridLogMessage << "\tCompSol " << CompSolutionTimer.Elapsed() << std::endl;
|
||
return;
|
||
}
|
||
}
|
||
|
||
std::cout << GridLogMessage << "FlexibleGeneralisedMinimalResidual did NOT converge" << std::endl;
|
||
|
||
if (ErrorOnNoConverge)
|
||
assert(0);
|
||
}
|
||
|
||
RealD outerLoopBody(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi, RealD rsq) {
|
||
|
||
RealD cp = 0;
|
||
|
||
Field w(src._grid);
|
||
Field r(src._grid);
|
||
Field z(src._grid);
|
||
|
||
std::vector<Field> v(RestartLength + 1, src._grid);
|
||
|
||
MatrixTimer.Start();
|
||
LinOp.Op(psi, z);
|
||
MatrixTimer.Stop();
|
||
|
||
PrecTimer.Start();
|
||
Preconditioner(z, w);
|
||
PrecTimer.Stop();
|
||
|
||
LinalgTimer.Start();
|
||
r = src - w;
|
||
|
||
gamma[0] = sqrt(norm2(r));
|
||
|
||
v[0] = (1. / gamma[0]) * r;
|
||
LinalgTimer.Stop();
|
||
|
||
for (int i=0; i<RestartLength; i++) {
|
||
|
||
IterationCount++;
|
||
|
||
arnoldiStep(LinOp, v, z, w, i);
|
||
|
||
qrUpdate(i);
|
||
|
||
cp = std::norm(gamma[i+1]);
|
||
|
||
std::cout << GridLogIterative << "FlexibleGeneralisedMinimalResidual: Iteration " << IterationCount
|
||
<< " residual " << cp << " target " << rsq << std::endl;
|
||
|
||
if ((i == RestartLength - 1) || (cp <= rsq)) {
|
||
|
||
computeSolution(v, psi, i);
|
||
|
||
return cp;
|
||
}
|
||
}
|
||
|
||
assert(0); // Never reached
|
||
return cp;
|
||
}
|
||
|
||
void arnoldiStep(LinearOperatorBase<Field> &LinOp, std::vector<Field> &v, Field &z, Field &w, int iter) {
|
||
|
||
MatrixTimer.Start();
|
||
LinOp.Op(v[iter], z);
|
||
MatrixTimer.Stop();
|
||
|
||
PrecTimer.Start();
|
||
Preconditioner(z, w);
|
||
PrecTimer.Stop();
|
||
|
||
LinalgTimer.Start();
|
||
for (int i = 0; i <= iter; ++i) {
|
||
H(iter, i) = innerProduct(v[i], w);
|
||
w = w - H(iter, i) * v[i];
|
||
}
|
||
|
||
H(iter, iter + 1) = sqrt(norm2(w));
|
||
v[iter + 1] = (1. / H(iter, iter + 1)) * w;
|
||
LinalgTimer.Stop();
|
||
}
|
||
|
||
void qrUpdate(int iter) {
|
||
|
||
QrTimer.Start();
|
||
for (int i = 0; i < iter ; ++i) {
|
||
auto tmp = -s[i] * H(iter, i) + c[i] * H(iter, i + 1);
|
||
H(iter, i) = std::conj(c[i]) * H(iter, i) + std::conj(s[i]) * H(iter, i + 1);
|
||
H(iter, i + 1) = tmp;
|
||
}
|
||
|
||
// Compute new Givens Rotation
|
||
ComplexD nu = sqrt(std::norm(H(iter, iter)) + std::norm(H(iter, iter + 1)));
|
||
c[iter] = H(iter, iter) / nu;
|
||
s[iter] = H(iter, iter + 1) / nu;
|
||
|
||
// Apply new Givens rotation
|
||
H(iter, iter) = nu;
|
||
H(iter, iter + 1) = 0.;
|
||
|
||
gamma[iter + 1] = -s[iter] * gamma[iter];
|
||
gamma[iter] = std::conj(c[iter]) * gamma[iter];
|
||
QrTimer.Stop();
|
||
}
|
||
|
||
void computeSolution(std::vector<Field> const &v, Field &psi, int iter) {
|
||
|
||
CompSolutionTimer.Start();
|
||
for (int i = iter; i >= 0; i--) {
|
||
y[i] = gamma[i];
|
||
for (int k = i + 1; k <= iter; k++)
|
||
y[i] = y[i] - H(k, i) * y[k];
|
||
y[i] = y[i] / H(i, i);
|
||
}
|
||
|
||
if (true) {
|
||
for (int i = 0; i <= iter; i++)
|
||
psi = psi + v[i] * y[i];
|
||
}
|
||
else {
|
||
psi = y[0] * v[0];
|
||
for (int i = 1; i <= iter; i++)
|
||
psi = psi + v[i] * y[i];
|
||
}
|
||
CompSolutionTimer.Stop();
|
||
}
|
||
};
|
||
}
|
||
#endif
|